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Abstract

Ultrashort pulsed mode-locked lasers enable research at new time-scales and revolutionary technologies from bioimaging to materials processing. In general, the performance of these lasers is determined by the degree to which the pulses of a particular resonator can be scaled in energy and pulse duration before destabilizing. To date, milestones have come from the application of more tolerant pulse solutions, drawing on nonlinear concepts like soliton formation and self-similarity. Despite these advances, lasers have not reached the predicted performance limits anticipated by these new solutions. In this letter, towards resolving this discrepancy, we demonstrate that the route by which the laser arrives at the solution presents a limit to performance which, moreover, is reached before the solution itself becomes unstable. In contrast to known self-starting limitations stemming from suboptimal saturable absorption, we show that this limit persists even with an ideal saturable absorber. Furthermore, we demonstrate that this limit can be completely surmounted with an iteratively seeded technique for mode-locking. Iteratively seeded mode-locking is numerically explored and compared to traditional static seeding, initially achieving a five-fold increase in energy. This approach is broadly applicable to mode-locked lasers and can be readily implemented into existing experimental architectures.

Figures (6)

(a) The elements in the laser cavity are iteratively changed as a function of time in order to stabilize an evolving pulse. (b) Reaching a pulse state requires that the initial state seeding the pulse evolution lies within a region of attraction (dark blue) of the exact solution (white line) supported by that resonator state. Regions of attraction denote areas where a seed state can be pulled in to the steady state solution that is linked to that specific resonator state (x-axis). By incrementally changing the resonator state, the pulse generated in the previous resonator state can be made to lie within a region of attraction for the new state, and thus safely be transitioned into a new steady state pulse solution (y-axis). In standard designs when statically seeded states do not lie within an attraction region of the desired final resonator state, pulse formation is not observed. (c) The pulse state of a standard statically seeded mode-locked laser is shown as a function of time. (d) The pulse state and resonator state of an iteratively-seeded mode-locked laser with the same final resonator state as (c) are shown as a function of time.

Representative simulations of the spectral and temporal evolutions of a pulse for a resonator with the same final cavity parameters. (a) and (b) represent a standard static seeded resonator. (c) and (d) represent an iteratively seeded resonator.

Map of cavity configurations for a standard noise seeded (a–b) and an ISM (c–d) cavity. Dark blue regions in (a) and (c) denote stable cavity configurations whereas light blue regions in (a) and (c) denote configurations that do not produce stable pulse evolutions. The ISM simulations begin at the origin dot in a linear trajectory in (a) and (c) until reaching a designated end point (The figure represents results of 162 simulations arranged in a 9 × 18 point grid of GDD x Esat for each cavity type). Figures (b) and (d) represent energy contours of these simulations, showing that in this example, an ISM design can generate pulses with 5× more energy than in similar statically seeded designs initialized with either cavity noise, a broad several hundred picosecond long pulse representative of acousto-optic seeding, or picosecond scale cavity fluctuations reflective of table tapping.

After every change in cavity configuration for an evolving pulse in the ISM cavity, the pulse was allowed to settle before taking the next step. These simulations show that each cavity step in the ISM resonator is able to stabilize and pull the pulse in the previous cavity step into a steady state solution. A comparison with a static-seeded resonator is shown to demonstrate that at no point in the evolution of the static seeded system is a mode-locked state stabilized. (a) Temporal evolution of a pulse as a function of round trip in a static-seeded resonator; (b) Energy and pulse quality Q as a function of round trip number for a static-seeded resonator; (c) Temporal evolution of a pulse as a function of round trip in an iteratively-seeded resonator; (d) Energy and pulse quality Q as a function of round trip number for an iteratively-seeded resonator.

The route taken to a final resonator state determines whether a pulse will or will not form. Here, the temporal evolution of a pulse is shown for four different cavity routes which each have the same final resonator state, but only one of which stabilizes pulse formation. Path 1: Cavity group delay dispersion and saturation energy are both varied in a linear relationship; Path 2: Cavity group delay dispersion is linearly varied while saturation energy is held fixed; Path 3: Cavity group delay dispersion is held fixed while saturation energy is linearly varied. This case represents an analogue of gradually increasing the pump power in a noise-seeded laser cavity; Path 4: Cavity group delay dispersion and saturation energy are both held fixed representing a standard noise-seeded cavity.

(a) The pulse quality Q is shown as a function of round trip number for the four different cavity paths P1–P4 shown in Fig 5. (b) The pulse state (represented by the quantity Q X E) is shown as a function of cavity state (represented by the added group delay dispersion). The arrows point in the direction of time. Only Path 1, which varies both pulse energy and group delay dispersion at the same time, leads to stable pulse generation.